{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import powerlaw\n",
    "from fbm import FBM\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Following the original papers, our simulations of the MF model can be described as follows. \n",
    "\n",
    "# Before the evolution of prices, we generate an array of relative prices {x(t):t=1, 2, · · · , T}, drawn from the Student \n",
    "# distribution with αx =1.3 and σx =0.0024, and an array of signs {s(t): t = 1, 2, · · · , T} according to a fractional \n",
    "# Brownian motion with Hs = 0.75. \n",
    "\n",
    "# At each simulation step t, an order is generated, whose relative price and direction are x(t) and s(t), respectively. \n",
    "# If x(t) is not less than the spread, the order is an effective market order, resulting in an immediate execution with \n",
    "# a limit order waiting at the opposite best price. \n",
    "\n",
    "# Otherwise, the incoming order is an effective limit order, which is stored in the queue of the limit order book. \n",
    "# Then we scan the standing orders to check if any of them can be canceled, following exactly the same process in the MF model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Relative prices\n",
    "def generate_rel_prices(alpha_x, sigma_x, T):\n",
    "    relative_prices = stats.t.rvs(df=alpha_x, loc=0, scale=sigma_x, size=T, random_state=None)\n",
    "    return relative_prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Signs following a fractional Brownian Motion\n",
    "def generate_signs(Hs, T):\n",
    "    f = FBM(n=T, hurst=Hs)\n",
    "\n",
    "    # Generate a fgn realization\n",
    "    fgn_sample = f.fgn()\n",
    "    \n",
    "    signs = []\n",
    "    for i in range(len(fgn_sample)):\n",
    "        if fgn_sample[i] >= 0:\n",
    "            signs.append(1)\n",
    "        else:\n",
    "            signs.append(-1)\n",
    "    \n",
    "    return signs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Mike_and_Farmer(T, Hs, A, B, alpha_x, sigma_x, ask_limit_orders, bid_limit_orders):\n",
    "    signs = generate_signs(Hs, T)\n",
    "    relative_prices = generate_rel_prices(alpha_x, sigma_x, T)\n",
    "    \n",
    "    log_prices = []\n",
    "    log_returns = []\n",
    "    spreads = []\n",
    "    \n",
    "    time_entry_ask = len(ask_limit_orders)*[0]\n",
    "    time_entry_bid = len(bid_limit_orders)*[0]\n",
    "    lifetime = []\n",
    "    \n",
    "    delta_0_ask = []\n",
    "    delta_0_bid = []\n",
    "    best_ask = ask_limit_orders[0]\n",
    "    best_bid = bid_limit_orders[-1]\n",
    "    for ask in ask_limit_orders:\n",
    "        delta_0_ask.append(ask - best_bid)\n",
    "    for bid in bid_limit_orders:\n",
    "        delta_0_bid.append(best_ask - bid)\n",
    "    \n",
    "    for order in range(T):\n",
    "        relative_price_i = relative_prices[order]\n",
    "        sign_i = signs[order]\n",
    "        \n",
    "        best_ask = ask_limit_orders[0]\n",
    "        best_bid = bid_limit_orders[-1]\n",
    "        \n",
    "        pi_mtt = 0.5*(best_ask+best_bid)\n",
    "        spread = best_ask - best_bid\n",
    "        \n",
    "        if relative_price_i < spread: # Limit order\n",
    "            if sign_i >= 0: #Buy\n",
    "                log_price_i = relative_price_i + best_bid\n",
    "                delta_0 = best_ask-log_price_i\n",
    "                delta_0_bid.append(best_ask-log_price_i)\n",
    "                bid_limit_orders.append(log_price_i)\n",
    "                time_entry_bid.append(order)\n",
    "                time_entry_bid = [x for _,x in sorted(zip(bid_limit_orders,time_entry_bid))]\n",
    "                delta_0_bid = [x for _,x in sorted(zip(bid_limit_orders,delta_0_bid))]\n",
    "                bid_limit_orders.sort()\n",
    "                \n",
    "            else : #Ask\n",
    "                log_price_i = best_ask - relative_price_i\n",
    "                delta_0 = log_price_i-best_bid\n",
    "                delta_0_ask.append(log_price_i-best_bid)\n",
    "                ask_limit_orders.append(log_price_i)\n",
    "                time_entry_ask.append(order)\n",
    "                time_entry_ask = [x for _,x in sorted(zip(ask_limit_orders,time_entry_ask))]\n",
    "                delta_0_ask = [x for _,x in sorted(zip(ask_limit_orders,delta_0_ask))]\n",
    "                ask_limit_orders.sort()\n",
    "        \n",
    "        else : # Market order\n",
    "            if sign_i >= 0 and len(ask_limit_orders)>2: #Buy\n",
    "                lifetime.append(order-time_entry_ask.pop(0))\n",
    "                price = ask_limit_orders.pop(0)\n",
    "                delta_0_ask.pop(0)\n",
    "                log_prices.append(price)\n",
    "            elif sign_i < 0 and len(bid_limit_orders)>2: #Ask\n",
    "                lifetime.append(order-time_entry_bid.pop())\n",
    "                price = bid_limit_orders.pop()\n",
    "                delta_0_bid.pop()\n",
    "                log_prices.append(price)\n",
    "        \n",
    "        # Cancelling orders !!\n",
    "        N_a = len(ask_limit_orders)\n",
    "        N_b = len(bid_limit_orders)\n",
    "        N_t = N_a + N_b\n",
    "        N_imb_a = N_a/N_t\n",
    "        N_imb_b = N_b/N_t\n",
    "        best_ask = ask_limit_orders[0]\n",
    "        best_bid = bid_limit_orders[-1]\n",
    "        \n",
    "        i = 0\n",
    "        while i < len(ask_limit_orders) and len(ask_limit_orders)>2:\n",
    "            ask = ask_limit_orders[i]\n",
    "            delta_t = ask - best_bid\n",
    "            delta_0 = delta_0_ask[i]\n",
    "            y_t = delta_t/delta_0\n",
    "            p_c = A*(1-math.exp(-y_t))*(N_imb_a+B)/N_t\n",
    "                \n",
    "            u = np.random.uniform(0,1)\n",
    "            if u <= p_c:\n",
    "                lifetime.append(order-time_entry_ask.pop(i))\n",
    "                ask_limit_orders.pop(i)\n",
    "                delta_0_ask.pop(i)\n",
    "            else:\n",
    "                i += 1\n",
    "        \n",
    "        j = 0\n",
    "        while j < len(bid_limit_orders) and len(bid_limit_orders)>2:\n",
    "            bid = bid_limit_orders[j]\n",
    "            delta_t = best_ask - bid\n",
    "            delta_0 = delta_0_bid[j]\n",
    "            \n",
    "            y_t = delta_t/delta_0\n",
    "            p_c = A*(1-math.exp(-y_t))*(N_imb_b+B)/N_t\n",
    "            \n",
    "            u = np.random.uniform(0,1)\n",
    "            if u <= p_c:\n",
    "                lifetime.append(order-time_entry_bid.pop(j))\n",
    "                bid_limit_orders.pop(j)\n",
    "                delta_0_bid.pop(j)\n",
    "            else:\n",
    "                j += 1\n",
    "        \n",
    "        best_ask = ask_limit_orders[0]\n",
    "        best_bid = bid_limit_orders[-1]\n",
    "        pi_mt = 0.5*(best_ask+best_bid)\n",
    "        \n",
    "        log_returns.append(abs(pi_mt-pi_mtt))\n",
    "        spreads.append(best_ask-best_bid)\n",
    "    \n",
    "    return log_prices, log_returns, spreads, lifetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x286149c2f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Defining hyperparameters\n",
    "T = 100000\n",
    "alpha_x = 1.3\n",
    "sigma_x = 0.0024\n",
    "Hs = 0.75\n",
    "A = 1.12\n",
    "B = 0.2\n",
    "ask_lo = np.log(np.linspace(101,110,20)).tolist()\n",
    "bid_lo = np.log(np.linspace(90,99,20)).tolist()\n",
    "\n",
    "# Simulating the model\n",
    "log_prices, log_returns, spreads, lifetime = Mike_and_Farmer(T, Hs, A, B, alpha_x, sigma_x, ask_lo, bid_lo)\n",
    "\n",
    "# Plotting the prices of transactions\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "plt.rcParams['font.size'] = 15\n",
    "plt.plot(range(len(log_prices)), np.exp(np.array(log_prices)))\n",
    "plt.xlabel(\"Transaction time\")\n",
    "plt.ylabel(\"Transaction price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x286149c7240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "plt.plot(range(len(spreads)), np.exp(np.array(spreads)))\n",
    "plt.ylabel(\"Spread\")\n",
    "plt.xlabel('Simulation time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x286149c77f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "plt.plot(range(len(log_returns)), np.exp(np.array(log_returns)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def increments(delta):\n",
    "    increments = []\n",
    "    i=0\n",
    "    while i+delta<len(log_prices):\n",
    "        diff = math.exp(log_prices[i+delta])-math.exp(log_prices[i])\n",
    "        increments.append(diff)\n",
    "        i += 1\n",
    "    return increments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_increments(delta):\n",
    "    increments = []\n",
    "    i=0\n",
    "    while i+delta<len(log_prices):\n",
    "        diff = log_prices[i+delta]-log_prices[i]\n",
    "        increments.append(diff)\n",
    "        i += 1\n",
    "    return increments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28615aa1780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "ax = plt.gca()\n",
    "\n",
    "#sns.distplot(incr, bins=500, hist=True)\n",
    "incr = increments(1)\n",
    "plt.plot(range(len(incr)), incr)\n",
    "plt.title(\"Clustering de volatilité\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2861926f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(-0.05,0.05)\n",
    "\n",
    "plt.hist(log_increments(1), bins=500, color='r')\n",
    "#plt.hist(log_increments(10), bins=500, color='b')\n",
    "#plt.hist(log_increments(100), bins=500, color='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28619147080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0,100)\n",
    "\n",
    "plt.hist(lifetime, bins=1000, color='r')\n",
    "#plt.hist(log_increments(10), bins=500, color='b')\n",
    "#plt.hist(log_increments(100), bins=500, color='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28615af3710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0,0.05)\n",
    "\n",
    "plt.hist(spreads, bins=500, color='r')\n",
    "#plt.hist(log_increments(10), bins=500, color='b')\n",
    "#plt.hist(log_increments(100), bins=500, color='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def divide(mylist):\n",
    "    incrP = []\n",
    "    incrN = []\n",
    "\n",
    "    for l in mylist:\n",
    "        if l>0:\n",
    "            incrP.append(l)\n",
    "        elif l<0:\n",
    "            incrN.append(-l)\n",
    "            \n",
    "    return incrP, incrN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n",
      "C:\\Users\\ElAamrani\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py:697: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-6796c57e8e82>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Calculating exponent for heavy tails\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpowerlaw\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mspreads\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, data, discrete, xmin, xmax, verbose, fit_method, estimate_discrete, discrete_approximation, sigma_threshold, parameter_range, fit_optimizer, xmin_distance, **kwargs)\u001b[0m\n\u001b[0;32m    132\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    133\u001b[0m                 \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Calculating best minimal value for power law fit\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msys\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstderr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 134\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfind_xmin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    135\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    136\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m>=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36mfind_xmin\u001b[1;34m(self, xmin_distance)\u001b[0m\n\u001b[0;32m    231\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    232\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 233\u001b[1;33m         \u001b[0mfits\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfit_function\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmins\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    234\u001b[0m         \u001b[1;31m# logging.warning(fits.shape)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    235\u001b[0m         \u001b[0msetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;34m's'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfits\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36mfit_function\u001b[1;34m(xmin)\u001b[0m\n\u001b[0;32m    228\u001b[0m                            \u001b[0mdata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    229\u001b[0m                            \u001b[0mparameter_range\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparameter_range\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 230\u001b[1;33m                            parent_Fit=self)\n\u001b[0m\u001b[0;32m    231\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmin_distance\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpl\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0min_range\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    232\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, estimate_discrete, **kwargs)\u001b[0m\n\u001b[0;32m   1108\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1109\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mestimate_discrete\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mestimate_discrete\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1110\u001b[1;33m         \u001b[0mDistribution\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1111\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1112\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mparameters\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, xmin, xmax, discrete, fit_method, data, parameters, parameter_range, initial_parameters, discrete_approximation, parent_Fit, **kwargs)\u001b[0m\n\u001b[0;32m    605\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    606\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mparameter_range\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparent_Fit\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 607\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    608\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    609\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, data)\u001b[0m\n\u001b[0;32m   1132\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mdata\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'parent_Fit'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1133\u001b[0m             \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparent_Fit\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1134\u001b[1;33m         \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtrim_to_range\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmin\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxmax\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxmax\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1135\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1136\u001b[0m         \u001b[1;32mfrom\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mlog\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\envs\\tensorflow\\lib\\site-packages\\powerlaw.py\u001b[0m in \u001b[0;36mtrim_to_range\u001b[1;34m(data, xmin, xmax, **kwargs)\u001b[0m\n\u001b[0;32m   1912\u001b[0m     \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1913\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mxmin\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1914\u001b[1;33m         \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m>=\u001b[0m\u001b[0mxmin\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1915\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mxmax\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1916\u001b[0m         \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m<=\u001b[0m\u001b[0mxmax\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Calculating exponent for heavy tails\n",
    "\n",
    "results = powerlaw.Fit(spreads)\n",
    "print(results.power_law.alpha)\n",
    "print(results.power_law.xmin)\n",
    "#R, p = results.distribution_compare('power_law', 'lognormal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculating exponent for heavy tails\n",
    "\n",
    "results = powerlaw.Fit(log_returns)\n",
    "print(results.power_law.alpha)\n",
    "print(results.power_law.xmin)\n",
    "#R, p = results.distribution_compare('power_law', 'lognormal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hurst exponent \n",
    "\n",
    "from numpy import cumsum, log, polyfit, sqrt, std, subtract\n",
    "from numpy.random import randn\n",
    "def hurst(ts):\n",
    "    \"\"\"Returns the Hurst Exponent of the time series vector ts\"\"\"\n",
    "    # Create the range of lag values\n",
    "    lags = range(2, 100)\n",
    "\n",
    "    # Calculate the array of the variances of the lagged differences\n",
    "    tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]\n",
    "\n",
    "    # Use a linear fit to estimate the Hurst Exponent\n",
    "    poly = polyfit(log(lags), log(tau), 1)\n",
    "\n",
    "    # Return the Hurst exponent from the polyfit output\n",
    "    return poly[0]*2.0\n",
    "\n",
    "# Assuming you have run the above code to obtain 'goog'!\n",
    "print(\"Hurst(M&F):  %s\" %(hurst(log_prices)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# AVE Model\n",
    "T = 100000\n",
    "Hs = 0.88\n",
    "alpha_x = 1\n",
    "sigma_x = 2.7*10**(-3)\n",
    "A = 1.11\n",
    "B = 0.22\n",
    "ask_lo = np.log(np.linspace(101,110,30)).tolist()\n",
    "bid_lo = np.log(np.linspace(90,99,30)).tolist()\n",
    "\n",
    "p, r, s = Mike_and_Farmer(T, Hs, A, B, alpha_x, sigma_x, ask_lo, bid_lo)\n",
    "log_returns = r\n",
    "spreads = s\n",
    "\n",
    "E_r = np.mean(log_returns)\n",
    "sigma_r = np.std(log_returns)\n",
    "E_s = np.mean(spreads)\n",
    "sigma_s = np.std(spreads)\n",
    "\n",
    "print(\"mean of returns\", round(E_r*10**4,2))\n",
    "print(\"mean of spreads\", round(E_s*10**4,2))\n",
    "print(\"standard deviation of returns\", round(sigma_r*10**4,2))\n",
    "print(\"standard deviation of spreads\", round(sigma_s*10**4,2))\n",
    "#results = powerlaw.Fit(log_returns)\n",
    "#print(\"exponent of the power law of returns\", results.power_law.alpha)\n",
    "#results2 = powerlaw.Fit(spreads)\n",
    "#print(\"exponent of the power law of spreads\", results2.power_law.alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# AVE Model\n",
    "T = 100000\n",
    "Hs = 0.81\n",
    "alpha_x = 1.25\n",
    "sigma_x = 2.6*10**(-3)\n",
    "A = 0.89\n",
    "B = 0.22\n",
    "ask_lo = np.log(np.linspace(101,110,10)).tolist()\n",
    "bid_lo = np.log(np.linspace(90,99,10)).tolist()\n",
    "\n",
    "p, r, s = Mike_and_Farmer(T, Hs, A, B, alpha_x, sigma_x, ask_lo, bid_lo)\n",
    "log_returns = r[(T-40000):]\n",
    "spreads = s[(T-40000):]\n",
    "\n",
    "E_r = np.mean(log_returns)\n",
    "sigma_r = np.std(log_returns)\n",
    "E_s = np.mean(spreads)\n",
    "sigma_s = np.std(spreads)\n",
    "\n",
    "print(\"mean of returns\", round(E_r*10**4,2))\n",
    "print(\"mean of spreads\", round(E_s*10**4,2))\n",
    "print(\"standard deviation of returns\", round(sigma_r*10**4,2))\n",
    "print(\"standard deviation of spreads\", round(sigma_s*10**4,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#results = powerlaw.Fit(log_returns)\n",
    "#print(results.power_law.alpha)\n",
    "#print(results.power_law.xmin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#results2 = powerlaw.Fit(spreads)\n",
    "#print(results2.power_law.alpha)\n",
    "#print(results2.power_law.xmin)"
   ]
  }
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